Evaluate. $\dfrac{125^{^{\scriptsize -\dfrac{11}{12}}}}{125^{^{\scriptsize -\dfrac14}}}=$
Explanation: $\begin{aligned} \dfrac{125^{^{\scriptsize -\dfrac{11}{12}}}}{125^{^{\scriptsize -\dfrac14}}}&=125^{^{\scriptsize -\dfrac{11}{12}-\left(-\dfrac14\right)}} \\\\ &=125^{^{\scriptsize -\dfrac{11}{12}+\dfrac{3}{12}}} \\\\ &=125^{^{\scriptsize -\dfrac{8}{12}}} \\\\ &=125^{^{\scriptsize -\dfrac23}} \\\\ &=\dfrac{1}{125^{^{\scriptsize\dfrac23}}} \\\\ &=\dfrac{1}{\left(\sqrt[3]{125}\right)^2} \\\\ &=\dfrac{1}{5^2} \\\\ &=\dfrac{1}{25} \end{aligned}$ In conclusion, $\dfrac{125^{^{\scriptsize -\dfrac{11}{12}}}}{125^{^{\scriptsize -\dfrac14}}}=\dfrac{1}{25}$